Question

So sánh 2 phân số sau:

A=1000^9 +2/1000^9 -1 và B=1000^9 +1/1000^9 -2

 

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Answer 1

\(A=\frac{1000^9+2}{1000^9-1}=\frac{1000^9-1+3}{1000^9-1}=\frac{1000^9-1}{1000^9-1}+\frac{3}{1000^9-1}=1+\frac{3}{1000^9-1}\)

\(B=\frac{1000^9+1}{1000^9-2}=\frac{1000^9-2+3}{1000^9-2}=\frac{1000^9-2}{1000^9-2}+\frac{3}{1000^9-2}=1+\frac{3}{1000^9-2}\)

Vì \(1000^9-1>1000^9-2\Rightarrow\frac{3}{1000^9-1}< \frac{3}{1000^9-2}\Rightarrow1+\frac{3}{1000^9-1}< 1+\frac{3}{1000^9-2}\Rightarrow A< B\)

Vậy A < B